Skip to main content
SpringerLink
Log in

Analysis of the relation between properties of LDPC codes and the tanner graph

  • Coding Theory
  • Published:
Problems of Information Transmission Aims and scope Submit manuscript

Abstract

A new method for estimating the number of errors guaranteed to be corrected by a low-density parity-check code is proposed. The method is obtained by analyzing edges with special properties of an appropriate Tanner graph. In this paper we consider binary LDPC codes with constituent single-parity-check and Hamming codes and an iterative decoding algorithm. Numerical results obtained for the proposed lower bound exceed similar results for the best previously known lower bounds.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gallager, R.G., Low-Density Parity-Check Codes, Cambridge: MIT Press, 1963. Translated under the title Kody s maloi plotnost’yu proverok na chetnost’, Moscow: Mir, 1966.

    Google Scholar 

  2. Zyablov, V.V. and Pinsker, M.S., Estimation of the Error-Correction Complexity for Gallager Low-Density Codes, Probl. Peredachi Inf., 1975, vol. 11, no. 1, pp. 23–36 [Probl. Inf. Trans. (Engl. Transl.), 1975, vol. 11, no. 1, pp. 18–28].

    MATH  Google Scholar 

  3. Zigangirov, K.Sh., Pusane, A.E., Zigangirov, D.K., and Costello, D.J., Jr., On the Error-Correcting Capability of LDPC Codes, Probl. Peredachi Inf., 2008, vol. 44, no. 3, pp. 50–62 [Probl. Inf. Trans. (Engl. Transl.), 2008, vol. 44, no. 3, pp. 214–225].

    MathSciNet  Google Scholar 

  4. Lentmaier, M. and Zigangirov, K., Iterative Decoding of Generalized Low-Density Parity-Check Codes, in Proc. 1998 IEEE Int. Sympos. on Information Theory (ISIT’2008), Cambridge, USA, Piscataway, NJ, 1998.

  5. Lentmaier, M. and Zigangirov, K., On Generalized Low-Density Parity-Check Codes Based on Hamming Component Codes, IEEE Commun. Lett., 1999, vol. 3, no. 8, pp. 248–250.

    Article  Google Scholar 

  6. Boutros, J., Pothier, O., and Zémor, G., Generalized Low Density (Tanner) Codes, in Proc. IEEE Int. Conf. on Communications (ICC’99), Vancouver, Canada, 1999, vol. 1, pp. 441–445.

  7. Stiglmayr, S. and Zyablov, V.V., Asymptotically Good Low-Density Codes Based on Hamming Codes, in Proc. 11th Int. Sympos. on Problems of Redundancy in Information and Control Systems, St. Petersburg, Russia, 2007, pp. 98–103. Available at http://www.k36.org/redundancy2007/proceedings.php.

  8. Zyablov, V.V., Johannesson, R., and Lončar, M., Low-Complexity Error Correction of Hamming-Code-Based LDPC Codes, Probl. Peredachi Inf., 2009, vol. 45, no. 2, pp. 25–40 [Probl. Inf. Trans. (Engl. Transl.), 2009, vol. 45, no. 2, pp. 95–109].

    Google Scholar 

  9. Frolov, A.A. and Zyablov, V.V., Asymptotic Estimation of the Fraction of Errors Correctable by q-ary LDPC Codes, Probl. Peredachi Inf., 2010, vol. 46, no. 2, pp. 47–65 [Probl. Inf. Trans. (Engl. Transl.), 2010, vol. 46, no. 2, pp. 142–159].

    MathSciNet  Google Scholar 

  10. Zyablov, V.V. and Rybin, P.S., Erasure Correction by Low-Density Codes, Probl. Peredachi Inf., 2009, vol. 45, no. 3, pp. 15–32 [Probl. Inf. Trans. (Engl. Transl.), 2009, vol. 45, no. 3, pp. 204–220].

    MathSciNet  Google Scholar 

  11. Barg, A. and Mazumdar, A., On the Number of Errors Correctable with Codes on Graphs, IEEE Trans. Inform. Theory, 2011, vol. 57, no. 2, pp. 910–919.

    Article  MathSciNet  Google Scholar 

  12. Tanner, R.M., A Recursive Approach to Low Complexity Codes, IEEE Trans. Inform. Theory, 1981, vol. 27, no. 5, pp. 533–547.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    V. V. Zyablov & P. S. Rybin

Authors
  1. V. V. Zyablov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. S. Rybin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. V. Zyablov.

Additional information

Original Russian Text © V.V. Zyablov, P.S. Rybin, 2012, published in Problemy Peredachi Informatsii, 2012, Vol. 48, No. 4, pp. 3–29.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zyablov, V.V., Rybin, P.S. Analysis of the relation between properties of LDPC codes and the tanner graph. Probl Inf Transm 48, 297–323 (2012). https://doi.org/10.1134/S0032946012040011

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0032946012040011

Keywords

Search

Navigation